3.5.36 \(\int \frac {\coth ^2(a+b x)}{x} \, dx\) [436]

Optimal. Leaf size=15 \[ \text {Int}\left (\frac {\coth ^2(a+b x)}{x},x\right ) \]

[Out]

Unintegrable(coth(b*x+a)^2/x,x)

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Rubi [A]
time = 0.02, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {\coth ^2(a+b x)}{x} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[Coth[a + b*x]^2/x,x]

[Out]

Defer[Int][Coth[a + b*x]^2/x, x]

Rubi steps

\begin {align*} \int \frac {\coth ^2(a+b x)}{x} \, dx &=\int \frac {\coth ^2(a+b x)}{x} \, dx\\ \end {align*}

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Mathematica [A]
time = 0.29, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\coth ^2(a+b x)}{x} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[Coth[a + b*x]^2/x,x]

[Out]

Integrate[Coth[a + b*x]^2/x, x]

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Maple [A]
time = 1.70, size = 0, normalized size = 0.00 \[\int \frac {\left (\cosh ^{2}\left (b x +a \right )\right ) \mathrm {csch}\left (b x +a \right )^{2}}{x}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(cosh(b*x+a)^2*csch(b*x+a)^2/x,x)

[Out]

int(cosh(b*x+a)^2*csch(b*x+a)^2/x,x)

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Maxima [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(cosh(b*x+a)^2*csch(b*x+a)^2/x,x, algorithm="maxima")

[Out]

-2/(b*x*e^(2*b*x + 2*a) - b*x) + integrate(1/(b*x^2*e^(b*x + a) + b*x^2), x) - integrate(1/(b*x^2*e^(b*x + a)
- b*x^2), x) + log(x)

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Fricas [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(cosh(b*x+a)^2*csch(b*x+a)^2/x,x, algorithm="fricas")

[Out]

integral(cosh(b*x + a)^2*csch(b*x + a)^2/x, x)

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Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\cosh ^{2}{\left (a + b x \right )} \operatorname {csch}^{2}{\left (a + b x \right )}}{x}\, dx \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(cosh(b*x+a)**2*csch(b*x+a)**2/x,x)

[Out]

Integral(cosh(a + b*x)**2*csch(a + b*x)**2/x, x)

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Giac [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(cosh(b*x+a)^2*csch(b*x+a)^2/x,x, algorithm="giac")

[Out]

integrate(cosh(b*x + a)^2*csch(b*x + a)^2/x, x)

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.07 \begin {gather*} \int \frac {{\mathrm {cosh}\left (a+b\,x\right )}^2}{x\,{\mathrm {sinh}\left (a+b\,x\right )}^2} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(cosh(a + b*x)^2/(x*sinh(a + b*x)^2),x)

[Out]

int(cosh(a + b*x)^2/(x*sinh(a + b*x)^2), x)

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